On Generalized Riesz Type Potential with Lorentz Distance

Abstract

In this article, we defined the Bessel ultra-hyperbolic operator iterated k-times and is defined by square(k)(B) = [B-x1 + B-x2 + ... + B-xp - Bxp+1 - ... - Bxp+q](k), where p+q = n, B-xi = partial derivative(2)/partial derivative x(i)(2) + 2v(i)/x(i) partial derivative/partial derivative x(i), 2v(i) = 2 alpha(i) + 1, alpha(i) > -1/2 [4], x(i) > 0, i = 1,2, ..., n, k is a nonnegative integer and n is the dimension of the R-n(+). Furthermore we have generated the generalized ultra -hyperbolic Riesz potential with Lorentz distance. This potential is generated by the generalized shift operator for functions in Schwartz spaces.